Ott says that it's de fide that all human beings subject to Original Sin are subject to the law of death, giving Trent Sess 5 can 2 as his witness. Pohle/Preuss say it's "common teaching."

Trent.V.2:

If any one asserts, that the prevarication of Adam injured himself alone, and not his posterity; and that he lost for himself alone, and not for us also, the holiness and justice, received of God, which he lost; or that he, defiled by the sin of disobedience, has only transfused death, and pains of the body, into the whole human race, but not sin also, which is the death of the soul, let him be anathema; inasmuch as he contradicts the apostle, who says: By one man sin entered into the world, and by sin death, and so death passed upon all men, in whom all have sinned.

It seems clear to me that this is indeed what the quoted Bible verse is saying, but it's not clear to me that this is what the canon is saying.